Sunday, March 01, 2009

When you have a lot of frozen water, you not only have a lot of water, but you have gravitational effects, and lots of bouncy, bouncy if the stuff melts, which slightly changes the shape of the Earth.

The West Antarctic Ice Sheet (WAIS) is big enough, that if it goes away, these things and more have to be considered. In a recent Science report, Mitrovica, Gomez and Clark discuss how global sea levels would rise if the WAIS collapsed.

Most models of sea level rise are relatively unsophisticated. Clark and Lingle added gravitational and rebound effects. Sea levels in the far south, near the sheet DECREASE because the gravitational attraction of the ice sheet for sea water in the area and elastic rebound. The effects extends out as far north as Peru. The Science report adds some more spice to the model

The sea-level theory adopted by Clark and Lingle does not allowfor shoreline migration, including the inundation and adjustmentof regions vacated by grounded, marine-based ice cover, or anyfeedback onto sea level of Earth rotation changes. We show a projection based on a sea-level theory (6) that overcomesthese limitations. These results show a highly accentuated sea-levelrise in the oceans bordering North America and in the IndianOcean. Coastal sites in North America would experience a rise30% higher than the (effective eustatic value) EEV.

Figure B shows the results of their calculation and C the differences between the two

In particular, the collapseof the WAIS leads to a displacement of the south rotation poleof 100 m x EEV toward the West Antarctic; this shift drivesa sea-level rise in North America and the Indian Ocean and afall over South America and Asia relative to the EEV

Sea level at Washington, DC is 6.3 m (the Potomac is tidal up to Georgetown) 1.3 m higher than the generic 5 m from Clark and Lingle's model. The Capital is safe (but the front steps are wet). The White Houseboat will float.

A, as Eli said is the calculation of sea level rise if the WAIS collapses from Clark and Lingle, B is the calculation from Moitrovica, et al and C is the difference between them. See it's easy

For the probability of collapse we get the news report and the paper also several blogs (you can google).

Most believe unlikely within the next 200 years, but for sure eventually if greenhouse gases continue to increase. Unlikely means there is believed to be a small probability of it happening sooner. There are a few outliers

There is big fresh water ice sitting in fairly deep salt water. Sounds like a thermo-haline- density pump just waiting to startup. I look at how we were surprised by the sudden warming of ocean currents in the Arctic and Southern Greenland; and, the scarcity of good deep water current /temperature data around Antarctica and I think the “unlikely in 200 years” is more wishful thinking than a good estimate of risk.

We simply have not done enough sampling in the Southern to have reasonable confidence that we would have detected a warm, deep-water plume that could destabilize Antarctic ice. Look at Gilbert’s “Statistical Methods for Environmental Pollution Monitoring” and check my numbers yourself.

the orbital elements transmitted by the GPS satellites -- broadcast ephemeris -- are in a realization of the WGS84 datum, which is connected to the solid Earth, i.e, it's an ECEF (Earth Centered, Earth Fixed) coordinate frame.

Point coordinates wouldn't change (much) if the pole were to move to another location. Much of the GPS software would have to be rewritten however, to account for such a large difference between instantaneous and conventional pole -- many linearizations would break down :-)

Alternatively, one could define a conventional pole closer to the instantaneous one. And yes, then all point coordinates would change...

Everybody's coordinates are already changing, all the time. Mere centimeters per year, which is why you don't notice. Geodesists do.

:wq - thanks for the detailed explanation - out of curiosity, how much does the instantaneous pole differ from the conventional one normally? 100 meters seems like an awful lot given the typical precision of GPS. Also I have a hard time imagining a one-time shift in the conventional pole being handled well, but if it happened gradually I suppose we'd be ok with it. It's all a matter of time-scale and rate I guess?

Arthur, we have the polar motion, a quasi-circular motion with a radius of about 200 milli-arcseconds, i.e. 5 m, and dominant periods of one year -- the forced component, and 14 months -- the Chandler wobble, which has to do with the Earth being a deformable body. See Wikipedia.

Then there is the polar wander, meaning that the center of the circle slowly migrates away from its original location. Currently small, but the prediction of the article is that it would become 100 m for every metre of sea level rise (IIUC). This migration is already happening, but much smaller, due to the Laurentide postglacial rebound, asymmetric wrt the Earth axis of rotation.

The conventional pole (CIO) is the average position of the pole over a reference period, which used to be 1900-1905... but the definition may have changed since then, as currently VLBI is the technique of choice for monitoring polar motion, much preciser than astronomical latitude observations ever were.

100 m is a lot, but also a lot less than the 6,378,137 m of the Earth's radius. So typically used linearizations in GPS software -- which should handle polar motion anyway -- ought to remain valid. But that's a generic answer, and I'm pretty sure that some GPS code depends on the distance between CIO and true pole being less than 10 m...

Note BTW that in relative GPS as typically used in geodesy -- i.e., you measure the relative location of two stations -- the effect of polar motion mostly cancels. And in precise geodetic GPS with post-processing you download not only precise satellite ephemeris -- telling you where every satellite is in space at the moment of measurement -- but also precise Earth orientation parameters, i.e., polar motion and length-of-day variations in rotation rate.

David, no more GPS will be the least of our worries... and I agree with Anon that technology will do the job before ice melt does.

Eli, the asymmetric Arctic melt (if you don't mean Greenland) shouldn't do anything (to first order). For the same reason that it doesn't affect sea level: the ice doesn't move place, it just changes state ;-)

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Eli Rabett

Eli Rabett, a not quite failed professorial techno-bunny who finally handed in the keys and retired from his wanna be research university. The students continue to be naive but great people and the administrators continue to vary day-to-day between homicidal and delusional without Eli's help. Eli notices from recent political developments that this behavior is not limited to administrators. His colleagues retain their curious inability to see the holes that they dig for themselves. Prof. Rabett is thankful that they, or at least some of them occasionally heeded his pointing out the implications of the various enthusiasms that rattle around the department and school. Ms. Rabett is thankful that Prof. Rabett occasionally heeds her pointing out that he is nuts.